A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder is 7 feet from the wall. The foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. The location of the foot of the ladder at time t seconds is given by the parametric equations (7+ 2t,0).

I found the parametric equation for y(t) =√ 25^2 -(7+2t)^2

Calculate the average velocity of the top of the ladder on each of these time intervals (correct to three decimal places).

for y (0,9)s

Explanation:

the average velocity can be computed by using the derivative:

For this case we have

However, for a real result the values of t must be

that is, an allowed interval for t is (0,9)

hope this helps!!

Explanation:

Since:

---(1)

By compositive derivate:

d(YB)/dt =VB = L*(d[sin(α)]/dα)*(dα/dt) = L*cos(α)*dα/dt --- (2)

From the expresion (1):

if we call; u = (Xo + 2t)/L

Then: dα/dt = (dα/du)*(du/dt) = (d[arcCos(u)]/du)*(d[(Xo + 2t)/L]/dt)

Thus:

Finally:

Or, in cartesians:

small = small current large mag large current

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles